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17 votes
7 answers
2k views

Non-constructive proofs of decidability?

Are there examples of sets of natural numbers that are proven to be decidable but by non-constructive proofs only?
4 votes
1 answer
1k views

Transfinite induction vs induction in mathematics

What are the nontrivial theorems one can prove about natural numbers which need transfinite induction? By "need transfinite induction" I mean one can show that the statement is not provable in ...